Global well-posedness of the full compressible Hall-MHD equations

Tao, Qiang; Zhu, Canze

doi:10.1515/anona-2020-0178

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…In addition, recently the temporal decay of solutions to the full compressible Hall-MHD fluids has been also widely investigated; see [10,30,40,43,44] for examples. Our main result can be easily extended to the full case.…”

Section: Introductionmentioning

confidence: 99%

Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations

2022

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Recently, Gao and Yao established the global existence and temporal decay rates of solutions for a system of compressible Hall-magnetohydrodynamic fluids (Gao and Yao in Discrete Contin. Dyn. Syst. 36: 3077–3106, 2016). However, because of the difficulty of derivative loss in the nonlinear terms, Gao and Yao could not provide the temporal decay for the highest-order derivatives of classical solutions. In this paper, motivated by the decomposition technique of both low and high frequencies of solutions in (Wang and Wen in Sci. China Math. 65: 1199–1228 2022), we further derive the temporal decay for the highest-order derivatives of the strong solutions. Moreover, the decay rate is optimal, since it agrees with the solutions of the linearized system.

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Section: Introductionmentioning

confidence: 99%

Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations

2022

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Propagation of nonclassical shock waves in Hall-magnetohydrodynamics model of non-ideal fluids

Yadav,

Shukla

2024

Physics of Fluids

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We investigate the behavior of nonlinear waves in the Hall-magnetohydrodynamics model of non-ideal fluids with the van der Waals equation of state. It is shown that the Hall effect leads to the formation of a nonclassical shock wave that does not follow Oleinik's entropy condition and propagates as an undercompressive shock. The evolution of a rectangular pulse is discussed by solving a Riemann problem with initial data containing a pair of discontinuities. In particular, we provide a thorough discussion of interaction of various waves emerging from the discontinuities. It is observed that during this interaction, a nonclassical shock may transform into a classical sonic shock depending on the critical value of the Hall parameter. Furthermore, we analyze the effects of van der Waals parameters and the Hall parameter on various aspects of wave propagation, such as shock speed, shock strength, width of wave fan, and interaction time.

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Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect

Kawashima

Nakasato

Ogawa

2022

Math. Models Methods Appl. Sci.

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This paper is concerned with the mathematical modeling of electro-magneto-hydrodynamics and magnetohydrodynamics by taking account of the Hall effect. We discuss conservation laws, strict convexity of the negative entropy as a function of conserved quantities, and the associated energy form. Moreover, we investigate the dissipative structure and decay properties of the linearized systems as applications of the general theory developed in Umeda et al. [On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435–457] and Shizuta and Kawashima [Systems of equations of hyperbolic–parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249–275].

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Global well-posedness of the full compressible Hall-MHD equations

Cited by 3 publications

References 28 publications

Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations

Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations

Propagation of nonclassical shock waves in Hall-magnetohydrodynamics model of non-ideal fluids

Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect

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